Lixiang Weigh, and Thomas A. Lipo, “Investigation of 9-switch Dual-bridge Matrix Converter Operating under Low Output Power Factor”, U.S.A., IEEE ISA2003, vol. 1, pp. 176-181 which will be described later discloses a direct AC power converting apparatus including a clamp circuit. FIG. 12 shows the direct AC power converting apparatus disclosed in the Lixiang Weigh, and Thomas A. Lipo, “Investigation of 9-switch Dual-bridge Matrix Converter Operating under Low Output Power Factor”, U.S.A., IEEE ISA2003, vol. 1, pp. 176-181.
For the convenience of description in the present application, the reference characters in the figure do not always coincide with those in the Lixiang Weigh, and Thomas A. Lipo, “Investigation of 9-switch Dual-bridge Matrix Converter Operating under Low Output Power Factor”, U.S.A., IEEE ISA2003, vol. 1, pp. 176-181.
It is assumed that an IPM motor is provided at an output side of the direct AC power converting apparatus. When an inductance per phase which corresponds to the average value of an effective inductance of the IPM motor is defined as La, an overload current serving as a criterion for interrupting a current supply to the IPM motor is defined as i, a voltage between both ends of the clamp capacitor is defined as Vc, an electrostatic capacitance of the clamp capacitor is defined as Cc, an line voltage of a three-phase AC power source is defined as Vs, and it is assumed that all the power stored in three-phase inductors included in the IPM motor is regenerated to the clamp capacitor; the following relational expression is satisfied.
                    [                  Math          .                                          ⁢          1                ]                                                                                  1            2                    ⁢                      La            ⁡                          (                                                i                  2                                +                                                      (                                          i                      2                                        )                                    2                                +                                                      (                                          i                      2                                        )                                    2                                            )                                      =                              1            2                    ⁢                      Cc            ⁡                          (                                                Vc                  2                                -                                                      (                                                                  2                                            ⁢                      Vs                                        )                                    2                                            )                                                          (        1        )            
Accordingly, the voltage between both ends of the clamp capacitor is represented by the following expression.
                    [                  Math          .                                          ⁢          2                ]                                                            Vc        =                                                            3                2                            ⁢                              La                Cc                            ⁢                              i                2                                      +                          2              ⁢                              Vs                2                                                                        (        2        )            
FIG. 13 is a graph based on the expression (2), showing a relationship of the voltage between both ends of the clamp capacitor relative to the electrostatic capacitance of the clamp capacitor. For example, when the power supply voltage Vs is 400 V, the inductance La is 12 mH, the overload current i is 40 A, and the electrostatic capacitance of the clamp capacitor is 10 μF, the voltage Vc between both ends of the clamp capacitor is approximately 1800 V. The voltage value exceeds 1200 V which is the device rating of a transistor or a diode for 400V class of power supply voltage.
In order to suppress the voltage Vc between both ends of the clamp capacitor to approximately 750 V for example, the electrostatic capacitance of the clamp capacitor has to be equal to or larger than 200 μF, based on the expression (2) and FIG. 13.
On the other hand, as the electrostatic capacitance of the clamp capacitor is larger, an inrush current caused at the time of power-on increases. To be specific, for example, a series circuit in which a power source, a reactor, a resistor, and a capacitor are connected in series, is assumed as a one-phase series circuit. When an inductance of the reactor is defined as L, a resistance value of the resistor is defined as R, and an electrostatic capacitance of the clamp capacitor is defined as C, transmission characteristics of an output (current) relative to an input (power supply voltage Vs) in the series circuit is represented by the following expression.
                    [                  Math          .                                          ⁢          3                ]                                                                      G          ⁡                      (            s            )                          =                              ic            Vs                    =                      sC            ⁢                                          1                /                LC                                                              s                  2                                +                                  sR                  /                  L                                +                                  1                  /                  LC                                                                                        (        3        )            
By obtaining a response to a step input, the following expression is derived.
                    [                  Math          .                                          ⁢          4                ]                                                                      G          ⁡                      (            s            )                          =                              sC            ⁢                                          1                /                LC                                                              s                  2                                +                                  sR                  /                  L                                +                                  1                  /                  LC                                                      ⁢                          1              s                                =                                    1              /              L                                                      s                2                            +                              sR                /                L                            +                              1                /                LC                                                                        (        4        )            
Here, by performing an inverse Laplace transform to the expression (4) with 1/L=D, R/L=E, and 1/LC=F, the following expression is derived.
                    [                  Math          .                                          ⁢          5                ]                                                                      i          ⁡                      (            t            )                          =                              D            ω                    ⁢                      ⅇ                                          -                σ                            ⁢                                                          ⁢              t                                ⁢          sin          ⁢                                          ⁢          ω          ⁢                                          ⁢          t                                    (        5        )                                [                  Math          .                                          ⁢          6                ]                                                                      ω          =                                                                      4                  ⁢                  F                                -                                  E                  2                                                      2                          ,                                  ⁢                  σ          =                      E            2                                              (        6        )            
As the electrostatic capacitance C of the capacitor is larger, F decreases. D and E do not depend on the electrostatic capacitance C, and are constant. Therefore, as the electrostatic capacitance C of the capacitor is larger, ω decreases. Accordingly, as the electrostatic capacitance C of the capacitor is larger, the amplitude term D/ω excluding attenuation over time has a greater value. That is, the inrush current increases with the increase in the electrostatic capacitance C of the capacitor.
By obtaining the maximum value of the current when a value obtained by differentiating i(t) by time is 0 (i(t)′=0) based on the expression (5), the following expression is derived.
                    [                  Math          .                                          ⁢          7                ]                                                            t        =                              π            -            α                    ω                                    (        7        )            
At this time, the current has the maximum value. This maximum value can be recognized as the inrush current. FIG. 14 is a graph showing a relationship of the inrush current (i((π−α)/ω)) relative to the electrostatic capacitance C.
As described above, when the electrostatic capacitance of the clamp capacitor is set at 200 μF in order to suppress the voltage between both ends of the clamp capacitor charged by a regenerative current to approximately 750 V, the maximum value (inrush current) of the current reaches 150 A, based on the expressions (6) and (7).
As techniques related to the present invention, Specification of U.S. Pat. No. 6,995,992, Japanese Patent Application Laid-Open No. 2006-54947, Japanese Patent Application Laid-Open No. 8-079963 (1996), and Japanese Patent Application Laid-Open No. 2-65667 (1990) are disclosed.